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A graph that consists of t cliques sharing a vertex v is said to be a t-friendship graph with center v. A friendship graph is a graph that is t-friendship for some . We solve the problem of finding the best upper bound for the size of a greedy 2-friendship decomposition and a greedy friendship decomposition of graphs of order n.

Purpose: The purpose of this paper is to suggest an Index entitled {GResilient} Index to assess the greenness and resilience of the automotive companies and corresponding supply chain. Design/methodology/approach: An integrated assessment model is proposed based on Green and Resilient practices. These practices are weighted according to their importance to the automotive supply chain competitiveness. The Delphi technique is used to obtain the weights for the focused supply chain paradigms and corresponding practices. The model is then tested using a case study approach in the automotive supply chain. Findings: The case study results confirmed the applicability of this Index in a real-world supply chain. The results show that the Resilient supply chain management paradigm is the one considered as the one that more contributes for the automotive supply chain competitiveness. Research limitations/implications: The proposed Index was developed in the automotive sector context therefore it could not be adjusted to a different one. Future research could consider other aggregation methods for the Index construction. Practical implications: Supply chain participants will be able to evaluate the performance of their companies or supply chain in terms of Green and Resilient paradigms. Also, the Index can be effectively employed for functional benchmarking among competing companies and supply chains.

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Domain Specific Languages (DSLs) are claimed to increase productivity, while reducing the required maintenance and programming expertise. In this context, DSL usability by domain experts is a key factor for its successful adoption. Evidence that support those improvement claims is mostly anecdotal. Our systematic literature review showed that a usability evaluation was often skipped, relaxed, or at least omitted from papers reporting the development of DSLs. The few exceptions mostly take place at the end of the development process where fixing problems identified is too expensive. We argue that a systematic approach based on User Interface experimental validation techniques should be used to assess the impact of the new DSLs. The rationale is that assessing important and specially tailored usability attributes for DSLs early in language construction will ultimately foster a higher productivity of the DSL users. This paper, besides discussing the quality criteria, proposes a development and evaluation process that can be used to achieve usable DSLs in a better way.

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Supply chains in an attempt to be more competitive, are adopting new management paradigm. Among these paradigms there are four that deserve particular mention because of their importance to better {SC} performance: lean, agile, resilient and green. The main objective of this paper is to propose a set of supply chain management practices to become the {SC} more lean, agile, resilient and green, which were named {LARG} practices, and to suggest a conceptual model that makes possible to analyze the influence of these {LARG} practices on manufacturing supply chains performance. Also, a set of operational, economic and environmental performance measures are suggested.

The mechanism proposed by Evans to justify the selectivity obtained in Lewis acid catalyzed Diels-Alder reactions of cyclopentadiene with acyloxazolidinones has been generalized and used in the rationalization of selectivities obtained in many other systems. However, we recently proposed an alternative mechanism, on the basis of open-chain mono- and bicomplexes, that avoids the need for chelates and explains the selectivity obtained by Evans. In this manuscript we apply our proposal to the catalyzed conjugated addition of amines to acylimidazolidinones, reported by Cardillo, and we clearly show that aluminum chelates are not involved in the reaction, as they induce no selectivity, while Cardillo observed high experimental selectivities. Our data equally show that bicomplexes with carbonyl parallel orientation, proposed by Cardillo to justify the experimental selectivity with nonchelating Lewis acids, indeed induce the opposite selectivity and have also to be dismissed. On the other hand, our mechanistic proposal allows for the full rationalization of the data obtained by Cardillo with aluminum, boron, or zinc Lewis acids and supports our previous proposal on DA cycloadditions of dienes to Evans chiral auxiliary derivatives.